Joint ICTP-IAEA Workshop on Nuclear Reaction Data for Advanced Reactor Technologies May 2008

Transcription

1 944-5 Joint ICP-IAEA Workshop on ucler Rection Dt for Advnced Rector echnologies 9-3 M 8 eutron Induced Cross Section Mesurements. P. Schilleeeck Institute for Reference Mterils nd Mesurements Geel, Belgium

2 eutron Induced Cross Section Mesurements Workshop on ucler Rection Dt for Advnced Rector echnologies rieste, Itl, 9 3 M 8 peter.schilleeeck@ec.europ.eu Joint Reserch Centre (JRC IRMM - Institute for Reference Mterils nd Mesurements Geel - Belgium

3 eutron cross section mesurements (Prt Dt reduction nd uncertinties (Prt Eperimentl oservles Definitions nd terminolog itting mthemticl model to eperimentl dt Bsic opertions AGS Emple ISO Guide, Guide to the epression of uncertint in mesurement, Genev, Switerlnd, ISO,995 Mnnhrt, A Smll Guide to Generting Covrinces of Eperimentl Dt, Juni 98, PB-MRB-84.H. röhner, ucl. Sci. Eng. 6 (997-8

4 Eperimentl oservles 3 Eperimentl oservles rnsmission Rection ields Definitions nd terminolog itting mthemticl model to dt Bsic opertions AGS Emples

5 rnsmission 4 SAMPLE I 3 otl SAMPLE OU 3 otl Response / (/ns - BKG fit BKG points ep C in out C B B in out Response / (/ns - BKG fit BKG points O / ns O / ns..8 rnsmission eutron Energ / e

6 rnsmission : dt reduction 5 Smple in ( Ded time correction ( Bckground sutrction Smple out ( Ded time correction ( Bckground sutrction ep C in out C B B in out RRR Resonnce shpe nlsis e URR Correction for resonnce structure n n tot n e tot ( vr tot... ep ( n R ( n,e n e tot (E n de n ep e n tot

7 Rection ield : dt reduction 6 Rection mesurement lu mesurement ( Ded time correction ( Ded time correction ( Bckground sutrction ( Bckground sutrction Y ep r r C C r B B r RRR Resonnce shpe nlsis URR Correction for self-shielding nd multiple scttering ( c Y ep ( n R (,E (E Y (E de (n,r c Y r n n r n r n n ep

8 Ded time correction (/ t t t 3 t 4 t i- t i t i+ ime D t k t i C (t i s i o s i j t i jt k o is the numer of ursts Response (Counts / ns D C.5..5 Before Correction D C 3 h(n, t 5 m ime - Of - light / ns 7 Sstem ded time for on-line dt processing (time-of-flight + mplitude: Acqiris DC8 (digitier = 35 ns CAE 78B (digitier = 56 ns Conventionl sstem DAQ = 8 ns (without mplitude similr to digitiers Moore, ucl. Instr. Meth. 69 (98 45 Mihilescu et l., sumitted to IM A

9 Ded time correction (/ 8 Response (Counts / ns 3 h(n, t 5 m Before After (/. 3 ime - Of - light / ns

10 Bckground correction (/3 9 Response (counts / ns otl Bckground filters Averge lues it eutron Energ / e Blck Resonnce ilters Element Energ / e Ag 5.9 W 8.83 Co S 7. Detection Principles

11 Bckground correction (/3 O - spectrum / (/ns Ep. it. Blck Resonnces e Blck Resonnce ilters Element Energ / e Ag 5.9 W 8.83 Co S ime-of-light / s

12 Bckground mesurement (3/3 BR- filters detector

13 Definitions nd terminolog Eperimentl oservles Definitions nd terminolog Proilit nd sttisticl quntities Error nd Uncertint Propgtion of uncertinties itting mthemticl model to dt Bsic opertions AGS Emples

14 Proilit nd sttisticl quntities 3 P( theoreticl proilit densit function (PD of P(, theoreticl proilit densit function of (, Men P( d rince ( P( d Covrince P(, dd ( ( Correltion (,

15 Oserved sttisticl quntities 4 n oservtions,, n of vrile m oservtions (,, ( n, n of vrile (, Smple men n n i i Smple vrince Smple covrince s s n i n i n n i i n ij Smple correltion r(, s s s

16 unction of vriles : liner function 5 n oservtions,, n of vrile = f(,, n Liner function f( i k i i i Men f( i k i i i rince f( i f i j i i i j i i j

17 unction of vriles : non-liner function 6 lor epnsion ( st order! f f(i f( i (i i i i f( f( g ( i i i i i i g i f i Men f( i f( i rince f( g i f gi g j i i i j i i j

18 Mtri nottion 7 Liner function f( A ik f i k Men A rince A A on-liner function ( st order lor! Men f( f( f( G ( g,ik f i k sensitivit mtri design mtri rince G G

19 Error nd Uncertint (ISO Guide 8 Uncertint (dispersion (or width, lws > Uncertint is prmeter ssocited with the result of mesurement, tht chrcteries the dispersion of the vlues tht could resonl e ttriuted to the mesurnd Error (difference etween two quntities, cn e + or - Error is the result of mesurement minus true vlue of the mesurnd

20 Error 9 ep C in out C B B in out Sstemtic error Men tht would result from n infinite numer of mesurements of the sme mesurnd crried out under repetilit conditions minus true vlue of the mesurnd. he epecttion vlue of the error rising from sstemtic effect = Rndom error Result of mesurement minus the men tht would result from n infinite numer of mesurements of the sme mesurnd crried out under repetilit conditions. he epecttion vlue of rndom error =

21 Sstemtic error (ISO Guide If sstemtic error rises from recognied effect, the effect cn e quntified nd correction or correction fctor should e pplied. he uncertint on the correction fctor should not e quoted s sstemtic error. One should not enlrge the uncertint to compenste for sstemtic effect tht is not recognied!

22 Evlution of uncertint components pe A evlution Method of evlution of uncertint the sttisticl nlsis of series of oservtions Is otined from n oserved frequenc distriution pe B evlution Method of evlution of uncertint mens other thn the sttisticl nlsis of series of oservtions. Is otined from n ssumed proilit densit function (sujective proilit. he evlution is sed on scientific judgement heoreticl distriution Eperience from previous mesurement dt Dt provided in clirtion or other certifictes Propgtion of uncertinties comined uncertint G f G g,ik fi k non-liner prolem : pproimtion!

23 Emple : Counting eperiment pe A evlution Perform repeted mesurements nd record the numer of events in time t Clculte the uncertint from the stndrd devition of the oserved frequenc distriution n i n i pe B evlution : Poison sttistics he oserved quntit is distriuted s Poison distriution he uncertint is defined the stndrd devition of Poison distriution s

24 How to quote uncertinties 3 Evlution of uncertint components pe A : sttisticl nlsis of repeted mesurements pe B : scientific judgement All uncertinties re sttisticl! (uncertint due to counting sttistics, uncertint on the normlition, (correlted or not-correlted uncertinties Stndrd (u or epnded uncertint Stndrd uncertint : s p = p =.68 ( u with u n Epnded uncertint : p > P p p e.g. p =.96 p =.95 n

25 itting mthemticl model to dt 4 Definitions nd terminolog Eperimentl oservles itting mthemticl model to dt Lest squres Mimum likelihood Generlied lest squres method Bsic opertions AGS Emples

26 Centrl limit theorem 5 Centrl limit theorem: he sum of lrge numer of independent nd identicll-distriuted rndom vriles will e pproimtel normll distriuted If,, n re independent nd identicll distriuted with men nd vrince then : for lrge n : the distriution of i n i is the norml distriution with prmeters (, n P, d ep d with n

27 Centrl limit theorem 6 Generl: sed on mimum entrop principle röhner, ucl. Sci. Eng. 6 (997 ( or oservles with covrince mtri,..., n which re identicll distriuted with men P, d ep ( ( d det(

28 itting mthemticl model to dt 7 Prolem: n dt points (,,, ( n, n nd model function f(, tht in ddition to the vrile lso depends on k prmeters,, k with n>k. Solution: ( Lest squres : find the vector such tht the curve fits est the given dt in the lest squres sense, tht is, the weigthed sum of squres is minimied: ( (ep f(, (ep f(, ( Mimum likelihood: find the vector tht mimies the likelihood function. When the PD is the norml distriution : P, d ep (ep f(, (ep f(, d Lest squres method is equivlent to Mimum likelihood

29 Generlied lest squres 8 Input from eperiment : ep nd, ep nd Liner model on-liner model ( st order lor m f(, G g,ij fi j m f(, f(, o G ( o ( G G g,ij fi j ( G G (G G (G ep ( o (G G G ( f(,o ep (G G o (G G n der ijp (proceedings ESARDA solved itertion

30 Bsic opertions 9 Definitions nd terminolog itting mthemticl model to dt Bsic opertions (+, -,, Bckground ormlition it correlted dt AGS Emples

31 3 Bckground Emple: vector dimension = f(,, uncorrelted uncertinties from counting sttistics : = uncertint on ckground (not correlted with : = = A A k i ik f

32 3 Bckground 4, ( 4 ( -, - = (, ( +, -, (

33 Bckground 3 ( -, - = (, ( +, - Covrince Onl digonl terms 4

34 33 Propgtion of uncertinties : covrince v v 4 4( 4 ( -, - = (, ( +, - =(v,v (v +v = Covrince Onl digonl terms 4

35 34 ormlition Emple: vector dimension = f(,, uncorrelted uncertinties from counting sttistics : = uncertint on normlition (not correlted with : = not -liner

36 35 ormlition /, ( 4 4 / (, = (, = (, /, (

37 36 ormlition Covrince Onl digonl terms (, = (, = (, / 4 /

38 it correlted dt: common offset uncertint 37 nd re oservles of the sme quntit K which re deduced from the eperimentl dt (, ffected common offset error with uncertint nd men =. he covrince mtri for (, = ( -, - is : (, where nd re the uncorrelted uncertint components of nd (e.g. due to counting sttistics. he est vlue K is otined minimiing the epression: (, ( k (ep K (ep K

39 it correlted dt: common offset uncertint 38 Solution : ( k ( K (ep ep (, K he est vlue k: K (weighted verge with uncertint : K

40 it correlted dt: common normlition uncertint 39 nd re oservles of the sme quntit K which re deduced from the eperimentl dt (, ffected common normlition with uncertint nd men =. he covrince mtri for (, = (, with = is : (, where nd re the uncorrelted uncertint components (e.g. due to counting sttistics. he est vlue k is otined minimiing the epression: (, ( k (ep K (ep K

41 4 it correlted dt: common normlition uncertint Solution : he est vlue K: ( weighted verge with uncertint : Onl in cse ( is smll K pproches the weighted verge. Known s : Peelle s Pertinent Pule, see röhner SE 6 (997 Due to non-linerities ( K ( ( k ( ep, ( ep ( (

42 it correlted dt: common normliton uncertint 4 Solution : tret the normlition s seprte oservle Oservles: ( ep,, with covrince mtri (,, he function is : ( ep,, = (,K, K = f(,k (note = / (,, (, K re determined minimiing: (,, (,K (( ep,, (, K, K (( ep,, (, K,K

43 Emple 4 wo mesurements (, of vrile ech with % uncorrelted uncertint nd % uncertint on the clirtion fctor : =.5 =. Best vlue for?,.5 ( (.. Weighted verge (onl uncorrelted terms : Lest squre without covrince : Lest squres with covrince :.88.8 Lest squres with clirtion fctor s prmeter : Lest squres without covrince + dding u fterwrds :.54.45

44 Summr : = (C B (/ 43 Uncertinties C : digonl, uncorrelted uncertinties due do counting sttistics Poison (pe B, or preferl repeted mesurements (pe A B : ckground sutrction introduces correlted uncertinties : normlition introduces correlted uncertinties nd B cn e considered s due to sstemtic effects. he vlue for B nd re the sstemtic corrections. hese corrections hve their uncertinties (or etter covrince mtri ot correcting for nd/or B implies tht the vlue cn not e quoted!

45 Summr : = (C B (/ 44 Be creful with lrge uncertinties on the normlition. Quote ll the components involved in the dt reduction process Seprte s much s possile the components which crete correlted uncertinties Include the normlition in the model

46 45 Generl : i = f(,, n, c,,c m i : X onl uncorrelted uncertinties (counting sttistics c i : c correlted uncertinties (normlition, ckground, c Y n Y Y Y G G m n c... c... Y k i ik Y f g

47 Eperimentl oservles 46 = f(, d, C in, B in, C out, B out Y r = f( r, r, d, C r, B r, C, B C d B r counting sttistics (not correlted u d from lest squre fit of time intervl distriution lest squre fit (correlted uncertinties u.5 % (lternting sequences of in-out mesurements depends on method Borell et l., Phs. Rev. C 76 (7 465 r depends on method (relted to r (n, for totl energ principle with PHW u % r Borell et l. ucl. Instr. Meth. A577, (7 66

48 AGS: Anlsis of Generic O -Spectr 47 Rection ield rnsmission Y ep r C C r B B r C ded time corrected counts B ckground contriution normlition fctor ep C in out C B B in out Histogrm opertions + Covrince informtion (AGS Y ep + covrince ep + covrince input Rection models : Resonnce prmeters + covrinces Cross sections + covrinces

49 48 Uncertint propgtion in AGS : function of vectors,, nd prmeter vector : =(,, Uncertint propgtion results in:... D S S correlted prt dimension: n k uncorrelted prt digonl : n vlues n : length of vector k : numer of common sources of uncertinties AGS

50 49 Uncertint in AGS : = (,Y Y Y D Y D Y Y Y Y L S D S S = (, Y covrince mtri (smmetric & positive definite Y onl digonl terms : D Y = Y onl digonl terms dimension: n k n vlues (digonl = L L (Cholesk decomposition, Y : dimension n : dimension k Yu L : lower tringulr mtri

51 5 Emple : = Y Y D D Y Y Y Y Y S D S S = Y Y onl digonl terms : D Y = Y onl digonl terms, Y : dimension n : dimension dimension: n n vlues (digonl Y u Y

52 5 Uncertint in AGS : = (,, S S S S D D D L S D S S = (,, = L L,, : dimension n : dimension k dimension: n k k = k + k + k n vlues (digonl = S S + D dim S = n k = S S + D dim S = n k D D S S S S S S

53 AGS, ile formt 5 Covrince mtri Storge nd clculus n elements (e.g. 3k 8 tes 8 G! n mult. & sum. /step ( steps 8 flops! AGS representtion n (k+ elements (3k, corr. 5 M n (k+ mult. & sum./step ( steps 7 3 flops X D S

54 AGS commnds 53 gs_mpt gs_geta gs_gete gs_getxy gs_ddvl gs_vgr gs_func gs_idtc gs_divi gs_mult gs_lico gs_ener gs_fit gs_fp gs_edit gs_list gs_putx gs_scn Write onl commnds Crete n empt AGS file Import spectr from nother AGS file Import/interpolte evluted dt from n ED file Import histogrm dt from n ASCII file Red/Write commnds : Opertions on spectr Add constnt vlue to ll Y-vlues of spectrum Averge Y vlues per chnnel Clcultes the Y vlues for specil function Determine the ded time correction of O-spectrum Divide spectrum nother Multipl spectrum with nother Liner comintion of n spectr with n constnts Build energ from O X-vector on-liner fit of spectr User-progrmmed function Red Onl commnds Edit constnts nd sclers ttched to spectrum List Y vlues of spectr with common X vlues Eport finl result to n ASCII file Scn the contents of n AGS file

55 AGS, Script for trnsmission dt 54 # crete gs-file gs_mpt RAK # red smple out scler=oout,cmout gs_getxy RAK /SCALER=$scler /ROM=spout.his /ALIAS=SOU # red smple in scler=oin,cmin gs_getxy RAK /SCALER=$scler /ROM=spin.his /ALIAS=SI /LIKE=ASOU # ded time correction dtcoef=dcoe gs_idtc RAK,ASOU /DIME=$dtcoef /LPSC= gs_idtc RAK,BSI /DIME=$dtcoef /LPSC= # normlie to centrl monitor nd divide in width gs_vgr RAK,CSOU /CMSC= gs_vgr RAK,DSI /CMSC= C C in out B B in out #clculte ckground contriution gs_func RAK /U=f /PARILE=PAROU /ALIAS=SBOU /LIKE=ASOU gs_func RAK /U=f /PARILE=PARI /ALIAS=SBI /LIKE=ASOU #sutrct ckground gs_lico RAK,ESOU,GSBOU /ALIAS=SOUE /PAR=.,-. gs_lico RAK,SI,HSBI /ALIAS=SIE /PAR=.,-. #crete trnsmission fctor gs_divi RAK,ISOUE,JSIE /ALIAS=RAK

56 Clcultion of trnsmission fctor 55 Smple in Smple out 5 C in B in 5 C out B out 4 4 Counts 3 ep in out C C B B in out Counts 3 ime / s. ime / s rnsmission fctor ime / s

57 Output AGS_PUX 56 B in / B in :. % B out / B out : 5. % / :.5 % C = D + S = D + S S X L X H u D S u B in B out E-.59E-.35E-4.4E- -.8E-.5E E-.67E-.45E-4.8E- -.E-.5E E-.73E-.54E-4.E- -.E-.5E E-.78E-.6E-4.4E- -.3E-.5E E-.7E-.5E-4.5E- -.5E-.45E E-.E-.4E-4.53E- -.4E-.4E E-.93E-.86E-4.54E- -.E-.35E E-.84E-.7E-4.55E- -.8E-.3E E-.76E-.57E-4.56E- -.5E-.5E E-.77E-.59E-4.57E- -.6E-.5E E-.85E-.73E-4.58E- -.9E-.9E E-.98E-.97E-4.6E- -.3E-.35E E- 3.75E- 4.6E E- -.8E-.5E E- 3.89E- 5.3E-4 4.4E- -.3E-.5E E- 3.8E- 4.46E-4 4.5E- -.3E-.5E E- 3.77E- 4.3E E- -.E-.5E-

58 AGS Output -> Covrince mtri 57 ime-of-flight / ns ime-of-flight / ns

59 O - spectrum / (/ns B 5.9 e = + O C B Blck Resonnces ime-of-light / s Emple : 3 h(n, in URR CRP IAEA h-u fuel ccle 5 Y Y,ep,ep r C B C B ( n, c Y,ep r C B 3 h(n, 3 C B C B B B B = o B + B ime-of-light / s 58 B B A. Borell et l. SE 5 (6-4 nmrn eutron Energ / ke

60 Emple : 3 h(n, in URR Correlted uncertinties due to ckground in cpture dt 59 E min E m,u ke ke m (% (% A. Borell et l. SE 5 (6-4

61 Emple : 3 h(n, in URR 6 ded time, ckground + normlition (.5% E min E m,u ke ke m (% (% A. Borell et l. SE 5 (6-4

62 Importnce of covrince dt 6 Appliction of rection model to deduce model prmeters: REI, SAMMY resolved resonnce prmeters IACS verge resonnce prmeters Minimie s function of prmeters (resonnce prmeters,ep ( (ep M( (ep M( Covrince of prmeters (G,ep G Covrince of clculted M G,M G

63 Averge resonnce prmeters from dt in URR 6 ep : < > verge cpture cross section Model : Generlied SLBW in URR : nd verge rdition width for =, ep =.6% nd =. u =.6 % c =. % ep =.6% nd =.9 u =.5 % c =.5 %.8 % % %..97 %. E n / ke,m (%,M (% Sirkov et l., Annls of ucler Energ, 8doi:.6/j.nucene.7..8,

64 Summr 63 Error uncertint Rndom error : epecttion vlue = Sstemtic error (correction fctor : epecttion vlue = All uncertinties re sttisticl Evlution of uncertinties pe A : sttisticl nlsis of repeted mesurements pe B : scientific judgment Importnce of covrince informtion Quote ll components involved in the dt reduction process which crete correlted uncertinties AGS, reduction of O-dt with propgtion of correlted nd uncorrelted uncertinties including full reporting of the reduction process